Predictive coarse-graining

JOURNAL OF COMPUTATIONAL PHYSICS

卷:333

Article

Schoeberl, Markus¹  Zabaras, Nicholas^2,3  Koutsourelakis, Phaedon-Stelios¹ 

[1] Tech Univ Munich, Continuum Mech Grp, Boltzmannstr 15, D-85748 Garching, Germany

[2] Tech Univ Munich, Inst Adv Study, Lichtenbergstr 2a, D-85748 Garching, Germany

[3] Univ Notre Dame, Dept Aerosp & Mech Engn, 365 Fitzpatrick Hall, Notre Dame, IN 46556 USA

关键词: Coarse-graining;    Generative models;    Bayesian;    Uncertainty quantification;    SPC/E water;    Lattice systems;   

DOI  :  10.1016/j.jcp.2016.10.073

来源: Elsevier

【 摘 要 】

We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to coarse map, we adopt the opposite strategy by prescribing a probabilistic coarse-to-fine map. This corresponds to a directed probabilistic model where the coarse variables play the role of latent generators of the fine scale (all-atom) data. From an information-theoretic perspective, the framework proposed provides an improvement upon the relative entropy method [1] and is capable of quantifying the uncertainty due to the information loss that unavoidably takes place during the coarse-graining process. Furthermore, it can be readily extended to a fully Bayesian model where various sources of uncertainties are reflected in the posterior of the model parameters. The latter can be used to produce not only point estimates of fine-scale reconstructions or macroscopic observables, but more importantly, predictive posterior distributions on these quantities. Predictive posterior distributions reflect the confidence of the model as a function of the amount of data and the level of coarse-graining. The issues of model complexity and model selection are seamlessly addressed by employing a hierarchical prior that favors the discovery of sparse solutions, revealing the most prominent features in the coarse-grained model. A flexible and parallelizable Monte Carlo - Expectation-Maximization (MC-EM) scheme is proposed for carrying out inference and learning tasks. A comparative assessment of the proposed methodology is presented for a lattice spin system and the SPCJE water model. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free